If Seriphyn is killling nothing but Serpentis in endless level 4 missions, I don't see why he would be hated by anyone but the Serpentis.
Because even Serpentis have families, friends, associates.
Yes they do. So do all the people everywhere that the Serpentis operatives hurt every day doing their 'job'. There are countless millions of people in the cluster that get fucked over by Serpentis, Angels or whatever on a daily basis, and all those people would love it if the Serpents would just go away or die or leave them alone. If Seriphyn, or BB, or whoever, wipe out a whole Serpentis battlefleet the widowed family members and/or orphaned kids back in Fountain will be very sad. But all those families all over the Fed and beyond who hear of this will more likely than not be happy for the news.
My character would be a fool to baseline in Fountain anywhere or on any Serpentis or Angel owned stations, unless he brought a large force of guards armed for nothing less than war, but baselining in the Fed and the most that would happen is likely some Serp. assassin, or angry 'associate' or some-such. Most who know of him or even care would likely want to buy him drinks because he killed all those people who were responsible for X injustice or whatever.
At the end of the day, the widows of Fountain are the same as the widows of Solitude - they blame different factions for their loss however, and report to different leaders, whose motives are very different. Ultimately, it's all the ones in a leadership position who are to blame for the cycle of hatred. Or whoever they hire to do their dirty-work...